Finite Group Databasebeta

← C3×#2273⋊C3 #11919640

Subgroups — C3×#2273⋊C3 #11919640

Order 1152.

416 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2273C311yesmaximal, characteristic, complemented
2#2273⋊C3C313yesmaximal, direct product factor
3C2×C3×C22⋊A4—41nomaximal
4C2×C3×C42⋊C3—42nomaximal
5C3×#95⋊C3—42nomaximal
6C22×C3×C22⋊C4—31no—
7C3×C4×C22⋊C4—32no—
8C3×C4×C22⋊C4—32no—
9C3×C22⋊A4—41no—
10C3×C42⋊C3—42no—
11#2273C3211yescharacteristic, complemented, Sylow
12C25×C3A411yescharacteristic
13C2×C22⋊A4—43no—
14C23×C3×C4—31no—
15C23×C3×C4—31no—
16C2×C3×C22⋊C4—34no—
17C2×C3×C22⋊C4—38no—
18C2×C3×C42—32no—
19C2×C3×C42A412yescomplemented
20C2×C42⋊C3—46no—
21C3×#95—32no—
22C3×#95A412yescomplemented
23#95⋊C3—46no—
24C2×C3×A4—164no—
25C2×C3×A4—161no—
26C22×C22⋊C4—31no—
27C4×C22⋊C4—32no—
28C4×C22⋊C4—32no—
29C24×C3—31no—
30C24×C3—34no—
31C24×C3—41no—
32C24×C3—121no—
33C22⋊A4—43no—
34C22×C3×C4—32no—
35C22×C3×C4—32no—
36C22×C3×C4—34no—
37C22×C3×C4—34no—
38C22×C3×C4—121no—
39C22×C3×C4—122no—
40C22×C3×C4—121no—
41C3×C22⋊C4—316no—
42C3×C42—42no—
43C3×C42—122no—
44C42⋊C3—46no—
45C3×A4—164no—
46C3×A4—161no—
47C25C3×A411yescharacteristic
48C23×C4—31no—
49C23×C4—31no—
50C2×C22⋊C4—34no—
51C2×C22⋊C4—38no—
52C2×C42—32no—
53C2×C42C3×A412yescomplemented
54#95—32no—
55#95C3×A412yescomplemented
56C23×C3—34no—
57C23×C3—32no—
58C23×C3—34no—
59C23×C3—62no—
60C23×C3—61no—
61C23×C3—61no—
62C23×C3—124no—
63C23×C3—124no—
64C23×C3C42⋊C314yescomplemented
65C23×C3C22⋊A411yescharacteristic
66C2×A4—163no—
67C2×A4—1612no—
68C2×C3×C4—34no—
69C2×C3×C4—34no—
70C2×C3×C4—62no—
71C2×C3×C4—64no—
72C2×C3×C4—62no—
73C2×C3×C4—124no—
74C2×C3×C4—124no—
75C2×C32—641no—
76C24—31no—
77C24—34no—
78C24—41no—
79C24—121no—
80C22×C4—32no—
81C22×C4—32no—
82C22×C4—34no—
83C22×C4—34no—
84C22×C4—121no—
85C22×C4—122no—
86C22×C4—121no—
87C22⋊C4—316no—
88C42—42no—
89C42—122no—
90C22×C3—31no—
91C22×C3—31no—
92C22×C3—34no—
93C22×C3—44no—
94C22×C3—62no—
95C22×C3—62no—
96C22×C3—64no—
97C22×C3—64no—
98C22×C3—124no—
99C22×C3#99711yescharacteristic
100A4—1612no—
101A4—163no—
102C3×C4—64no—
103C3×C4—64no—
104C32—641noSylow
105C23—34no—
106C23—32no—
107C23—34no—
108C23—61no—
109C23—62no—
110C23—61no—
111C23—124no—
112C23—124no—
113C23C3×C42⋊C314yescomplemented
114C23C3×C22⋊A411yescharacteristic
115C2×C4—34no—
116C2×C4—34no—
117C2×C4—62no—
118C2×C4—64no—
119C2×C4—62no—
120C2×C4—124no—
121C2×C4—124no—
122C2×C3—31no—
123C2×C3—31no—
124C2×C3—64no—
125C2×C3—643no—
126C2×C3C22⋊(C42⋊C3)11yescharacteristic
127C22—31no—
128C22—31no—
129C22—34no—
130C22—44no—
131C22—62no—
132C22—62no—
133C22—64no—
134C22—64no—
135C22—124no—
136C22C3×#99711yescharacteristic
137C4—64no—
138C4—64no—
139C3—643no—
140C3#2273⋊C311yescharacteristic, direct product factor
141C2—31no—
142C2—31no—
143C2—64no—
144C2C3×C22⋊(C42⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C22⋊(C42⋊C3)
commutator, cosocle, hypocenter#2273C32
FrattiniC23C3×C22⋊A4
FittingC3×#2273C3
socleC23×C3C22⋊A4
LCSG ▷ #2273
UCSC1 ◁ C2×C3

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#2273C3semidirect
2. #2273⋊C3C3direct (N × H)
11. #2273C32semidirect
19. C2×C3×C42A4semidirect
22. C3×#95A4semidirect
53. C2×C42C3×A4semidirect
55. #95C3×A4semidirect
64. C23×C3C42⋊C3semidirect
113. C23C3×C42⋊C3semidirect
140. C3#2273⋊C3direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#22733
#2273⋊C33
C2×C3×C22⋊A44
C2×C3×C42⋊C34
C3×#95⋊C34